Systems Thinking for the Control of Phenomena: How to Construct a Control System

Abstract

A very relevant and useful class of systems that Systems Thinking deals with are control systems. This chapter examines the concept, structure and typology of control systems by using the logic and language of Systems Thinking.

Appendices

Appendix 3.1 A Bit of “Unpretentious” Robotics: A Robot in Motion in “n” Dimensions

A particularly interesting control system – in terms of its diffusion in nature and its infinite application possibilities – is that which allows the movement of a point in a “space” formed by any number “n” of dimensions.

For a space of n = 4 dimensions – defined by the coordinates S = (X, Y, Z, W) – the system can be described as the control problem involving the transfer of a point P = (x, y, z, w), defined in S, toward a different point, assumed to be the objective, P* = (x*, y*, z*, w*).

In fact, the shifting of P toward P* in a space of n = 4 dimensions involves eliminating the distance between P* and P based on the typical logic of control.

To achieve this we must change the position of the intercepts for each of the four coordinates.

There is an infinite number of strategies to carry out this change of position. Management could decide to change the position of P by acting first on the coordinate X, and then on Y, and so on. Or it could start by shifting W, then Z, and so on.

A very simple (holonic-type) strategy would be to transform the unitary control system into four lower-level control systems, considering the coordinates P* as basic objectives which are acted on by four control levers, one for each coordinate. Each lower-level control system determines and eliminates the shifting of coordinate P with respect to P*, which is considered to be the objective.

The result is the gradual shifting of P toward P*, as shown in Fig. A.3.1.1, where the transfer – with the parameters indicated in the control panel – is carried out over 90 periods.

Fig. A.3.1.1

Dynamics of a point P toward an objective P*

We must decide if and when P will reach P* in order to allow the lower-level systems to stop their action.

We need only return to the first-level control system and calculate the Euclidean distance between P* and P, which is defined as:

$$ {{\hbox{P}}^{*}} - {\hbox{P}} = \sqrt {{{{{({{\hbox{X}}^{*}} - {\hbox{X}})}}^2} + {{{({{\hbox{Y}}^{*}} - {\hbox{Y}})}}^2} + {{{({{\hbox{Z}}^{*}} - {\hbox{Z}})}}^2} + {{{({{\hbox{W}}^{*}} - {\hbox{W}})}}^2}}} $$

The first-level control system stops when P* – P = 0; this occurs when the four second-level control systems, each acting autonomously, eliminate the distance in each coordinate, thereby allowing the first-level system to shift the point from P to P*.

Figure A.3.1.1 shows a control system that shifts point P₀ = (0, −20, −50, −20) toward the objective P* = (180, 160, 150, 100) through four second-level systems that carry out the shift along the axes, with the action rates and reaction times specified in the system’s control panel in the line “shift”.

The last column of the table in Fig. A.3.1.1 shows both the shifting of point P toward P*, which is reached at time 90 when the distance is eliminated, and the shiftings of the point along the four coordinates.

An actual example of this type of control system, with only three dimensions, is the mobile shifting point of a crane with a fixed vertical boom. The shifting point is moved to the objective point by actions on the three coordinates by means of the angular rotation of the crane shaft, the horizontal shifting of the cab, and the vertical shifting of the winch.

We can easily see that every movement of our hands or other parts of our body to reach a point-objective is, in fact, produced by the actions of individual translatory muscles which, though acting in a single direction, give the impression of a continuous movement, just as occurs in the model in Fig. A.3.1.1.

A variant of this is a control system with four dimensions in which, along with the three spatial dimensions, there is a fourth dimension: time. Each vehicle travelling in three-dimensional space that must move from one spatial point to another within a set time interval acts according to this logic.

We can also consider two systems of motion, say A and B, and set a rule that A follows a route toward its spatial and temporal objectives, set by its governance, while B follows A, taking as it objective reaching, at each “t”, A’s position, as shown in Fig. A.3.1.2.

Fig. A.3.1.2

Dynamics of two systems of pursuit in a three-dimensional space

What we have here is a true system of pursuit of B toward A.

A’s spatial route (fleeing) and B’s (pursuing), moving at a “fixed pace”, can be easily perceived from the initial graph in Fig. A.3.1.2. (obtained with Mathematica from the Wolfram Research Company); this graph shows the route (succession of points in space) the two systems take in three-dimensional space from two different perspectives.

We can easy transform the previous system of pursuit into a collision system because system B can be programmed to collide with A, or to anticipate or follow it.

Robotics represents a very interesting field of application for systems of movement. In particular, Cartesian robots – which can, for example, move a utensil placed at the tip of a mobile arm from one point to another in three-dimensional Cartesian space – have the features of typical systems of movement.

Two robots programmed to move an object from one to the other – a utensil, or a work component – can be viewed for all intents and purposes as systems of collision; if, however, they must place their object at a certain distance from the other, then they are queueing systems.

Cartesian robots can also be viewed as control systems of more than three dimensions.

Consider, for example, an industrial robot that must move an object from point PA to PB over a given time, that is, with a certain speed, by rotating it in a certain way and carrying out three processes within a given time interval, using for this three different tools the robot itself chooses from its own catalogue. In this case we can imagine a control system of seven dimensions (objectives): the three spatial dimensions, the speed of the movement (time of movement), the degrees of rotation of the transporting head, the manufacturing time, and the catalogue of tools. The spatial objectives can also be dynamic, as in the case of robots that must follow a given path (which is nevertheless defined) or must construct things using different tools that change when the objective-result so requires.

Appendix 3.2 Viable Systems as Control Systems

This section we will consider, in synthesis, Stafford Beer’s model, which is universally recognized as the Viable System Model, or VSM (Beer 1979, 1981). This model interprets organizations as viable systems that are open, recursive and adaptable and that, thanks to their cognitive and control structure, which is capable of communicating with the economic and non-economic environment, tend to endure for a long time through continual adaptation, even in the presence of disturbances not foreseen at the time of the system’s design and implementation (see Sect. 3.3).

The VSM outlined in Fig. A.3.2.1 characterizes the vital organization as a structure composed of five interconnected sub-systems (SS):

Fig. A.3.2.1

A synthesis of the Viable System Model

• ss1: operations. This represents the operational units, which in turn are viable systems whose purpose is to achieve the operational objectives at the various levels by connecting with the environment, to which they are structurally coupled; the operational units that make up the SS1 are unquestionably Control Systems oriented toward objectives and specific and particular constraints, both internal and external.

• ss2: coordination. The operational units of SS1 – which employ common resources and are potentially in competition regarding the objectives – are interconnected Control Systems which are usually interfering systems that can thus produce, in their local values, an oscillatory dynamics that may cause inefficiencies. For this reason SS2 is charged with coordinating the interconnected operational units according to a logic entirely analogous to the one illustrated in Fig. A.3.2.1.

• ss3: control. The operational units of SS1 each pursue local objectives. They must therefore be directed toward the achievement of the higher-order objectives, which refer to the organizational unit, based on a common programme. The SS3 are charged with this function. The same term used by Beer – the SS of control – clearly reveals that SS3 is a typical Control System based on planning. Since it is capable of activating a range of control levers, SS3 is charged with formulating the utilization strategies of the levers for the various objectives. Nevertheless, SS3 cannot detach itself from subsystems SS4 and SS5, as it forms together with them a higher-order subsystem that carries out cognitive activities and represents the organization’s intelligence.

• ss4: research of information on the environment (intelligence). The survival capacity and vitality conditions of the organization depend on the latter’s capacity to continually observe the environment and forecast its “future” state in order to allow SS3 to formulate programmes of action to which it adapts the units and activities of SS1. SS4 represents the viable system element charged with proposing the vital objectives – based on foreseeable future scenarios – and translating these into programmes of action whose implementation it oversees.

• ss5: policy. To complete the VSM, Beer has clearly observed that organizations are multi-objective Control Systems. Thus the control lever strategies used by the lower-order subsystems are not sufficient; instead, a careful assessment and rational ordering of SS4 objectives is indispensable. SS5 is necessary precisely to guarantee that the organization will have a unitary management, an entrepreneurial along with a managerial capacity that can define the policies needed to achieve the vital objectives.

In short, with the VSM Beer recognizes that in order to be vital the organization-firm must operate as a unitary Control System, such as the one outlined in Fig. A.3.2.2, where the operational organs are arranged in a holarchy of Control Systems.

Fig. A.3.2.2

The VSM as a Control System

According to Beer, the VSM can also be applied to the organs, groups of organs, or operational units however defined, that compose the organization, which itself thus appears composed of lower-level viable systems. Moreover, every organization must always be viewed as part of a larger organization. Beer proposes the following “theorem” which, on the one hand, clarifies the holonic nature of every organization, and on the other highlights the recursiveness of the holarchies (Mella 2009a).

Recursive system theorem. In a recursive organizational structure, any viable system contains, and is contained in, a viable system. There is an alternative version of the Theorem as stated in Brain of the Firm, which expressed the same point from the opposite angle: ‘if a viable system contains a viable system, then the organizational structure must be recursive’ (Beer 1979, p. 118).

Appendix 3.3 Dashboards in Performance Control Systems

In his Viable System Model, Stafford Beer observed that the higher up we go in the managerial structure the more the decisions and controls are based on synthetic data. Conversely, the more we descend toward the operational base of the organization, the more the decisions and controls are based on analytical data. For example, each warehouse manager analytically controls the stock levels and stock reorderings entrusted to him; the director of supplies bases his assortment decisions on the synthetic data he gets from the analytical data the warehouse managers periodically provide him; the head of production, in planning the production schedules, relies on synthetic data that comes from both the supply manager and the sales manager.

It is immediately clear that, in order to decide on and control the operations and actions that produce the economic and financial variables, the integral data that is summarized by the dynamics of an entire observation period (e.g., sales, revenues, outstanding debts of an entire month or quarter) are not particularly significant. On the other hand, the data that allows management to understand, possibly in real time, the dynamics of the underlying phenomena it wants to control (the trend in sales, revenues, outstanding debts) is necessary, in order to quickly perceive the deviations with respect to the objectives.

Precisely for this reason there has been a spread in the technique for building dashboards (management cockpits, or tableau de bord).

These instruments are not at all new from a conceptual point of view. Modern technology has made them easy to build, powerful from an informational point of view, and particularly effective for management at all levels in guiding the company (or its sectors).

We can list among the oldest dashboards the daily summary of business drawn up by the first medieval merchants. More recently, the accounting reports prepared daily, weekly and monthly can be interpreted as, for all intents and purposes, true dashboards through which management uses summary data of management operations produced by the general accounting department: for example, not the individual credits but the trends in overall credits, daily, weekly, monthly, and so on., with all the possible meaningful aggregate figures, reports and indices.

The most complete modern “global” dashboard is the system of reports provided by the reporting activities.

This process, at different levels of analysis and synthesis and with various frequencies, prepares ordered and summary reports to provide management with the final statements regarding the program implementation, to be compared with the budget values in order to determine the deviations which, when analyzed in terms of volume, price and mix deviations, etc., represent the basis for decisions to regulate the control activities.

These initial forms of dashboard have several clear limits. Firstly, they mainly show economic and financial values, ignoring other significant quantitative data (e.g., absenteeism or downtime for machinery in the various departments, stock levels, motivation, customer loyalty, etc.). Furthermore, they do not include summary indicators (ROE, ROI, stock rotation, length of credits and debits, etc.). Above all, they present “too much” data without selecting that which is most relevant for managerial control decisions at the various levels of the control structure.

Today various types of specialized dashboards have been introduced in different contexts, and these present only the data that involves specific functions or sectors.

For example, hypermarkets use dashboards that show the flow of the most important goods (stocks, supplies, average supply times, average time of shelf display, sales, shortages, thefts, etc.). Big hospitals create dashboards for the daily control of the operational dynamics of the main clinics or departments (flows and types of admissions, length of waiting lists, average time of stay, types of treatments, failure percentage, multiple interventions, quantity of drugs administered daily, daily consumption of medications, etc.).

In terms of control theory we must consider dashboards as, in fact, instruments for continual reporting in order to monitor a system of performance objectives and of standards to attain in order to permit the control of operations, and of the operators, at a specific operational level (Otley 1999).

The dashboard data can also be generally defined as key performance indicators (KPI), since it monitors the performance set as the objective in the control process, as shown in the model in CLD A.3.3.1.

CLD A.3.3.1

Dashboard as control instrument

Figure A.3.3.1 shows an attractive graph of a dashboard for top management.

Fig. A.3.3.1

Prototypical executive sales dashboard with a KPI Report (Source: InetSoft Technology Corp. www.inetsoft.com/company/kpi_dashboard)

The Balanced Scorecard (BSC) is a particular kind of dashboard, destined for top management, which was created by Kaplan and Norton (1992) as an instrument for monitoring the strategic performance of the entire firm and evaluating its progress toward the objective of creating shareholder value, set by the shareholders.

Limiting myself here to a brief description, this dashboard was conceived of to permit a continuous evaluation of performance from four strategic perspectives (areas, or focuses) held to be fundamental for permitting management to have a “balanced” perception of the organization’s performance:

• 1. Financial,

• 2. Customer,

• 3. Internal Business Processes,

• 4. Learning and Growth.

Each perspective, represented by a scorecard, is assigned a relative weight, and for each one a limited number of measures are included in the BSC, from among those the manager considers to be truly significant, as shown in Fig. A.3.3.2, which is taken from Kaplan and Norton (2001, p. 375).

Fig. A.3.3.2

Weights and measures of the BSC perspectives

The following are usually considered to be particularly efficient measures to choose for any perpsective:

• 1. Measures for the financial perspective: value of the action, growth in profits, profit rate, ROI, EVA, ROE, operating costs, operating margin, corporte objectives, survival, profitability, growth, cost reduction, increase in ROI, cash flow, earnings, increase in earnings, profit rate of shares, and so on (Mella 2005b);

• 2. Measures for the client perspective: service level, market share, new clients, new products, new markets, customer satisfaction, customer loyalty, product reliability, perceived quality of the product and/or collateral services, customer complaints, etc.;

• 3. Measures for the internal perspective: increase in efficiency, quality of processes, utilization rate of production capacity, stock storage period, waste, recycling rate of production waste, remanufacturing, lead time, average unit cost, employee morale, motivation, and so on;

• 4. Measures for the learning and growth perspective: trend in value creation, product diversification, supplier diversification, increase in R&D, risk diversification, strengthening of internal control, development of new products, continual improvement, technological leadership, employee involvement, etc.

According to Kaplan and Norton, these perspectives and measures are the best for guiding management in its strategic performance evaluation, even if, in particular contexts, they can be supplemented by others, or enriched by new measures:

The four perspectives could be viewed as a scheme of reference and not as a straightjacket. Many organizations use the BSC and establish relative weights for each of the scorecard measures. These relative weights are used to evaluate performance (Kaplan and Norton 1996, p. 34).

Olve is even more explicit:

If, as we have indicated, the scorecard could guide us in growing our business, then it is natural to believe it possible to change the number of perspectives, areas, or focusses (Olve et al. 1999, p. 120).

The BSC, originally conceived of as a dashboard, has been transformed in recent years into a true strategic planning instrument. To this end, as shown in Fig. A.3.3.3, each perspective is assigned a scorecard specifying the objectives and specific targets, along with the respective measures for achieving them.

Fig. A.3.3.3

The BSC as a strategy-forming instrument (adapted from Kaplan and Norton 1996, p. 76)

If also used as an instrument for strategy formulation and not only to monitor its implementation, the BSC takes on the twofold role of objective to achieve and measures to obtain, allowing management to measure the deviations between the planned strategy and the actual one.

Appendix 3.4 The Control of Projects with Grid Programming: CPM and PERT

Projects are viewed as a set of activities – systematically linked and characterized by specific sequences, length, cost and quality level – which must be completed within a certain time period and meet a pre-established overall cost and quality. To respect the objectives of length, cost, and quality it is indispensable to have an accurate planning of the entire project and a continual control of the progress of the activities.

All firms have projects, more or less complex, but some are specialized in the production of projects by contracting out. This is known as production by contracting out and includes:

• The construction of specific and unique products: for example, publishing a book, making a film, constructing a machine, setting up an assembly line;

• The production of large works (construction) such as skyscrapers, stadiums, bridges, ships, missiles;

• The study of a prototype and the launch of its production;

• Carrying out an advertising or marketing campaign.

Every project, due to its uniformity and the large investment that is needed, require three forms of control:

• 1. The control of the project’s quality and efficiency in order to guarantee it is carried out according to the qualitative characteristics that make it appropriate for use by the consumer (use or functional objective);

• 2. The control of time efficiency in order to verify that the time factor of both the overall project and its successive phases is respected; careful planning is needed to carry out the project in the minimum time allowed, given the technical length of the various activities, the user’s needs and the constraints from the producer’s equipment capacity;

• 3. The control of economic efficiency to verify that implementation costs are respected; the project planning must guarantee that the project is achieved with the minimum cost, given the efficiency objectives and the coordination needs regarding other projects under way at the same time.

These three forms of control considered together represent the main phases of project management, whose objective is optimizing and coordinating the projects, shortening the implementation times of the most urgent activities, and assigning these the resources taken from the non-urgent projects, whose duration can be lengthened without compromising the overall duration of the entire project.

In order to control and optimize projects various techniques have been developed for representing the projects, the most widespread of which are the Gantt Diagrams developed by Henry Gantt around 1910 – in order to build sequential models, or chrono programs, of the project; the CPM, developed in 1957; and the PERT, in 1958. The latter two techniques build grid models of the project, or activity maps, that provide a view of the links between the activities rather than their chronological timing (Woolf 2007).

Today these three techniques are joined in a single grid technique called PERT/CPM, which is integrated by the Gantt Diagrams; this grid is produced by Microsoft Project™ or other software easy to find on the internet that makes it easy to apply to grids (for example, www.criticaltools.com/pertmain.htm (Kerzner 2003)).

Very briefly, temporal economic control entails the following steps:

• 1. Analyzing the activity to carry out;

• 2. Building the grid of activities for the project, a model that presents in a reciprocal relationship the various activities that constitute the project, precisely specifying the order relationships among the activities themselves and determining the initial and final event of the entire project;

• 3. Estimating the length of time and cost of the various phases;

• 4. Calculating the length of time and cost of the entire project;

• 5. Optimizing the activities in order to reduce length of time and costs;

• 6. Scheduling the implementation of the activities (Gantt Diagrams);

• 7. Optimizing the workloads of the personnel and the machines.

The control of projects through CPM and PERT is based on the idea that the duration of an activity, which requires the use of resources over time, depends on the quantity of resources needed to carry out the activity, and thus on the cost, according to an inverse relationship. In order to reduce the duration it is necessary to increase the quantity of resources per unit of time; vice-versa, a reduction in resources leads to an increase in the duration of any activity. It is thus possible to control the duration by modifying the cost, or to control the cost by increasing the activity’s duration.

The basic difference between these two techniques is in the method for estimating the duration of the activities. CPM produces a deterministic estimate, while PERT a probabilistic one, identifying three durations: pessimistic, normal and optimistic, and taking their weighted average, with the normal estimate having a weight four times that of the pessimistic and optimistic ones.

Figure A.3.4.1, which represents the map of the phases (in summary form) of a project to launch a new product, allows us to observe the basic elements of grid planning:

Fig. A.3.4.1

The grid for a simple product-launching project

• (a) The eight blocks – indicated by E₁, E₂, … E₈ – show the events that represent the states of progress of the project;

• (b) Each event (state of progress) is marked by a date that places it sequentially with respect to the events that precede it; by convention, the initial event is assigned the date [0];

• (c) The nine arrows – indicated by A, B,… I – represent the (macro) activities that produce progress in the implementation (state of progress) of the project;

• (d) Each arrow (activity) is characterized by a length of implementation – in specific time units (days, weeks, months, etc.) – written in italics next to the name of the activity;

• (e) The date of each event (state of progress) of the project (block) is determined by the sum of the activity durations, the succession of which form a chain that, starting from the initial event, leads to that event;

• (f) When the same event is produced by several chains of activities, then the date of the event is determined by the duration of the longest chain that reaches it; for example, E₄ is dated [19] since the date is determined by the longer of the two chains that reach it: [A → B → C], with duration 19, and [A → I], with duration 7;

• (g) Through this procedure we determine the date of the final event, which represents the date for the conclusion of the entire project; that is, its duration;

• (h) The chain of activities (shown by the thicker arrows) that determines the final date – in this case, [A → E → F → G → H], with duration [34] – is called the critical path, since lengthening the execution by only a single time unit of one of its activities would lengthen the overall length of the project; vice-versa, to reduce the duration of the project, the length of execution of some critical activities is necessary;

• (i) The execution of the critical activities, which form the critical path, must thus be specially controlled;

• (j) It is clear that the activities that lie on the non-critical chains are subject to possible shifting as regards both the initial and ending dates as well as, and above all, the length of execution; PERT defines as slack or float time the amount of time that a non-critical activity can be delayed without causing a delay in the entire project; the non-critical activities can be carried out more slowly, thereby reducing their float time and providing them with fewer resources per unit of time.

For such simple projects the calculations can be carried out in an equally simple manner. However, PERT/CPM provides concrete algorithms to automatically quantify length, costs and slack times, even for projects with hundreds or thousands of activities.

With knowledge of the resources used for the various activities, the consequent length of the activities and the qualitative standards of the work undertaken, it is possible to control the project through a system of control systems that reflect the project model itself: for each activity a micro control system is developed to monitor the length, cost, and quality of execution; a broader system concerns the various chains in the project, and with even broader synthesis we can construct the macro control system of the entire project.

This macro control system is not only multi-lever (Sect. 3.5) but also multi-objective in a true sense (Sect. 3.6), since the contracting firms must verify contemporaneously the achievement of the objectives regarding length, cost, and quality agreed to with the commissioning firm; usually, the control of the objective interferes with that of the other objectives.

As can be seen in the project in CLD A.3.4.1, a shortening of the overall duration can lead to greater cost and often to a decline in the level of quality. Thus, it is fundamental to prioritize the objectives.

CLD A.3.4.1

Multi-objective system of control for projects

In projects involving, for example, the prevention or remedy of damage from great disasters, as well as defense projects, there is usually great urgency, and preference is thus given to the time objectives. The cost of carrying out space and medical projects is quite significant, and there is thus a frequent extension in length, or even the abandonment, of projects whose cost has become too onerous with respect to the initial objectives.

In typically business projects all three objectives are relevant, and a policy establishing the priorities must be set at the beginning.

It is interesting to note that CLD A.3.4.1 has the same structure as the control system for an airplane illustrated in CLD 3.15.

To carry out the control, several classes of control levers can be used:

• 1. Varying the quantity/quality of the resources assigned to each activity in order to control the duration and quality of the critical and non-critical activities (operational lever);

• 2. Varying the starting date of the activities, especially the non-critical ones, by optimizing the machine load and capacity needed for manufacturing, with appropriate algorithm assignments (operational lever);

• 3. Acting on the float times and on the non-critical activities in order to free up resources for the critical activities (operational lever);

• 4. Selecting appropriate suppliers and productivity increases in order to control the costs and quality of execution (extraordinary lever);

• 5. Redesigning the structure of the project (remapping) in order to modify the critical and non-critical chains, eliminating or merging certain activities (structural lever).

If the project extends over a vast horizon (activities carried out in various places) and a lengthy one (long duration), then there is greater probability that external disturbance events can alter the time, cost and quality of the activities.

When such events cause errors that cannot be eliminated with the control levers, it is necessary to recognize the impossibility of achieving the original objectives and to prepare a revision of the project for those parts that must still be achieved.