Motivated by PID control simplicity, robustness and validity to deal with the nonlinearity and uncertainties of dynamics, through simulating the intelligent behavior of human manual control, and only using the elementary information on hand, this paper introduces a simple formulation to represent prior knowledge and experiences of human manual control, and proposes a simple and practicable control law, named Human-Simulating Intelligent PID control (HSI-PID), and the simple tuning rules with the explicit physical meaning. HSI-PID control can not only easily incorporate prior knowledge and experiences of experts control into the controller but also automatically acquire knowledge of control experiences from the past control behavior to correct the control action online. The theoretical analysis and simulation results show that: HSI-PID control has the better flexibility, stronger robustness, and especially the faster self-learning ability, and it can make the motion of system identically track the desired response, whether the controlled system has the strong nonlinearity and uncertainties of dynamics or not, even under the actions of uncertain, varying-time and strong disturbances.
It is well known that the PID controllers [
A major drawback of PID control is that it often suffers a serious loss of performance, that is, causes large overshoot and long settling time, even may lead to instability due to unlimited integral action. To disguise this drawback, various PID-like control laws have been proposed to improve the transient performance. For example, a saturated-P, and differential feedback plus a PI controller driven by a bounded nonlinear function of position errors [
In 2009, general integral control [
Based on the statement above, it is obvious that the error,
where
Based on the cognition above, through simulating the intelligent behavior of human manual control, this paper proposes a simple and practicable control law, named Human-Simulating Intelligent PID control (HSI-PID). The main contributions are as follows: 1) a simple and practical formulation to represent prior knowledge and experiences of manual control is developed, and then it is easy to be used to design a controller; 2) the simple and practical tuning rules with the explicit physical meaning are introduced, and then it is easy to tune a high performance controller; 3) two kinds of fire new and simple integrator and integral control action is proposed, and then the intrinsic shortcomings of PID control is removed in principle; 4) HSI-PID control not only can easily incorporate prior knowledge and experiences of experts control into the controller but also can automatically acquire knowledge of control experiences from the past control behavior to correct the control action online, and then can make the motion of system identically track the desired response. Moreover, simulation results verify our conclusions again.
The remainder of the paper is organized as follows: Section 2 describes Human-Simulating PID control law and definitions. Section 3 presents the tuning rules of human-simulating intelligent PID control. Example and simulation are provided in Section 4. Conclusions are presented in Section 5.
An experienced operator will anticipate all types of disturbances to the system. It would be very difficult to reproduce in an automatic controller the many judgments that an average person makes daily and unconsciously. So it is more realistic for us to simulate the control procedure of the human manual control in order to obtain as nearly perfect operation as possible.
A general human manual control procedure can be described as follows: 1) when the error is large and the error tends to increase, the human controller produces a largest control action, and attempt to restrain the error to increase continuously; 2) when the error decreases, the human controller will gradually reduce the control action to limit the degressive rate of error for avoiding the system out of control; 3) when the error is small and tend to zero, the human controller produces a small or even inverted control action, and attempt to prevent the overshoot; 4) when the error is large, the human controller produces an inaccuracy control action, if the error is small, the human controller produces a precise control action; 5) the amplitude of control action is determined by the size of error and tendency that the error is changing.
Based on the statements above, it is easy to see that the human manual control law is in a good agreement with the sigmoid-type function. So, the sigmoid-type function can be used to simulating the procedure of human manual control, that is, approximating Equation (1).
For the purpose of this paper, it is convenient to introduce the following definition.
Definition 1. Tow Error [
In human manual control procedure: if
where
The schematic graph of Tow Error is shown in
Definition 2. Desired Acceleration [
In human manual control procedure, one usually has an explicit expectation for the speed of response and overshoot. Namely, under the control action, the error,
zero in the meantime. In another words, there is some kinds of the cooperative relationship between the error and its rate in human manual control procedure. For simulating the behavior of human manual control, it is indispensable to introduce the concept of Desired Acceleration,
where
Discussion 1. When the initial condition and parameter of Equation (3) is given, the desired velocity,
The schematic graph of Desired Acceleration is shown in
From Equation (3), if the controller output is assimilated to the force acting on the motion object, and using Newton’s laws of motion, the controller output,
where
Combining Equations (2) and (3) into Equation (4) results in PD-type Human-simulating intelligent control law, as follows:
Discussion 2. From
It is obvious that PD-type Human-simulating intelligent control law described by Equation (5) is not capable of reducing the error to zero and making the error strictly change along the desired law when a constant disturbances act on the controlled system. However, an experienced operator can automatically adjust the control output and produce an accurate control action to eliminate or reject all kinds of disturbances. This procedure can be described as follows: according to the current state of the controlled system and the former control experiences, the human controller produces a control action, if the control action just counteracts the disturbance action, and then he maintains the control action; if the control action is large, and then he decreases the control action, vice versa. In other words, through correcting the control action again and again, eventually the operator can make the error change along the desired law and stabilize the error at zero or acceptable limit, and then the control action tends to a constant or changes along with the change of disturbances.
Based on the statements above, it is easy to know that: 1) simulating the control procedure that human manual control eliminates or rejects all kinds of the disturbances is very challenging because the disturbances are often uncertain and varying-time; 2) human manual control is a procedure of automatically accumulating the control experiences, and self-adapting the action of all kinds of disturbances and uncertainties of dynamics by exploration. However, integral control just is of this kind of ability. So, for simulating the manual control behavior above, the integral action must be introduced into the control law, as follows:
where
Discussion 3. Compared to PID-like control and general integral control laws reported by [
1) The prior knowledge and experiences of manual control can be incorporated into the controller easily;
2) When
3) Just as the statement above, the basic principle of the integrator in (6) and (7) is similar with the general integrator in [
4) The integral control action is a compensation for the shortcoming of PD control action, or an accumulation of the past PD control action. This method to adjust integral action can be viewed as the accumulation of the past control experiences or learning from past control experiences;
5) Combining the demonstration above and Discussion 2, it is easy to see that the control laws (6) and (7) can strictly constraint the motion of system along the trajectories of desired response.
All these show that the control laws proposed here not only can easily incorporate prior knowledge and experiences of experts control into the controller but also can automatically acquire knowledge of control experiences from the past control behavior to correct the control action online, and then can make the motion of system identically track the desired response. Therefore, the control laws (6) and (7) should have more rapid adaptive or self-learning ability, better flexibility and stronger robustness, and can easily yield higher control performance. This is why it is called human-simulating intelligent PID control.
For practical applications in industrial control, it is very necessary and interesting to develop a simple and efficient method to tune the controller proposed here. So, the purpose of this section is to address the tuning rules of human-simulating intelligent PID control.
In the control laws (6) and (7), there are six parameters. The parameters,
From the control law (5), it is easy to know that: 1) when
where
The purpose that we introduce the integral action is to complete rejection of uncertain disturbances and dynamics of controlled system, and yield zero steady- state error. So, the integral action in the control laws is indispensable for most industrial control applications. This leads to that
In general, the settings above are usually close to the final values. However, a realistic expectation is that some tweaking of the parameters will be required to obtain a transient performance of high control. In practice, if the overshoot is large, which means that speed of response is too rapid or maximum of Tow Error is too small, and then we can fix
To illustrate the effect of the control laws, a two link manipulators shown in
where:
The normal parameter values of system are selected as:
The desired (set point) positions are chosen as:
when
The tangent hyperbolic function,
The simulations with sampling period of 1ms are implemented. Under the normal and perturbed parameters, the motion trajectories of Link1 and Link2 are shown in
From the simulation results, it is easy to see that: 1) the optimum response can be achieved by a set of control parameters in the whole domain of interest, even under the case that the payload is changed abruptly; 2) the motion trajectories shown in
that the motion of the system can identically track the desired response, whether the controlled system has the strong nonlinearity and uncertainties of dynamics or not, even under the actions of uncertain, varying-time and strong disturbances. All these demonstrates that: 1) HIS-PID controller not only can remove the intrinsic shortcomings of PID control but also has the faster self-learning ability, better flexibility and stronger robustness with respect to uncertain nonlinear system; 2) HIS-PID control not only can effectively deal with uncertain nonlinear system but also it is a powerful and practical tool to solve the control design problem of dynamics with the nonlinear and uncertain actions.
In this paper, a novel human-simulating intelligent PID control law is founded by simulating the intelligent behavior of human manual control. The main contributions are as follows: 1) the formulation to represent prior knowledge and experiences of manual control are very simple and practical, and then it is easy to be used to design a controller; 2) the simple and practical tuning rules with the explicit physical meaning are introduced, and then it is easy to tune a high performance controller; 3) two kinds of fire new and simple integrator and integral action are proposed, and then the intrinsic shortcomings of PID control are removed in principle; 4) the control laws proposed here not only can easily incorporate prior knowledge and experiences of experts control into the controller but also can automatically acquire knowledge of control experiences from the past control behavior to correct the control action online, and then can make the motion of system identically track the desired response. Moreover, simulation results verify our conclusions again.
For HSI-PID control, this paper is only a starting point and further cooperative research is needed to make progress in this area. For example, the design theory to ensure system stability is not developed.
Liu, Z.N. (2017) Human-Simulating Intelligent PID Control. International Journal of Modern Nonlinear Theory and Application, 6, 74-83. http://dx.doi.org/10.4236/ijmnta.2017.62007